A model-free test for independence between time series

The problem of assessing the independence of time series arises in many situations, including evaluating the spatial synchrony of populations in different locations over time. Tests for independence generally have relied on assuming a particular dynamic model for each of the series, and those that do not, require long series. We adapt a test for association between spatial processes to provide a model-free (MF) test for independence between two time series under the assumption that each series is stationary and normally distributed. We evaluate the performance of the test through simulations and compare it with the naive (N) test, which ignores serial correlations, as well as with tests based on residuals from fitting specific dynamic models. We also consider additional tests that involve bootstrapping the MF and N tests. We find that the MF test generally preserves the desired test size, although this is not the case in some extreme settings. The MF test is clearly superior to residual-based tests that arise from fitting an incorrect model. The bootstrap tests are not as robust as the general MF test, but when they are valid, they seem to be more powerful. We also examine the robustness of the procedure to the additional measurement errors present in many applications, explore the extent to which some deficiencies in the MF test are due to estimation of the unknown covariances, and investigate the effect of nonnormality on the MF test. We illustrate the MF test’s performance through an example assessing mouse populations from different locations.